If \(K\)  is a nonarchimedean field, we use the terms \(K\) -affinoid algebra and topologically of finite type (henceforth abbreviated tft) \(K\) -algebra synonymously; recall that these are exactly the Banach \(K\) -algebras that can receive a continuous surjection from a Tate algebra \(K\langle x_1,...,x_n \rangle \) . Likewise, we say “rigid space over \(K\) ” and “adic space locally of tft over \(\mathop {\mathrm {Spa}}K\) ” interchangeably. If \(A\)  is a tft \(K\) -algebra, we write \(\tilde{A} := A^\circ / A^{\circ \circ } = (A^\circ / t)^{red}\) ; this is a \(k\) -algebra of finite type [1]}, where \(k\)  is the residue field of \(K\)  and \(t\)  is a pseudouniformizer (i.e., any nonzero element of \(K^{\circ \circ } - \lbrace 0\rbrace \) ).
